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        <h1 id="影像变化检测研究综述"><a class="markdownIt-Anchor" href="#影像变化检测研究综述"></a> 影像变化检测研究综述</h1>
<p>多时相：不同时间获取的同一地域的一组影像、地图或地理数据<br />
变化检测：是通过对地物或现象进行多次观测从而识别其状态变化的过程</p>
<p>变化检测基本流程</p>
<ol>
<li>预处理：通过预处理步骤进行数据的配准和辐射校正，减弱外界成像环境影响从而简化 变化检测问题。</li>
<li>变化检测：分析多时相数据中地物的光谱、空间、纹理等特征差异，提取变化强度或 “from-to”变化类型等信息</li>
<li>阈值分割：将连续的变化强度利用阈值分割的方式转化为离散的变化信息，生成变化或未变化等语义结果。</li>
<li>精度评价：评价变化检测结果的精度</li>
</ol>
<p>多时相光学遥感影像是变化检测技术中使用最广泛的数据源，此外基于多时相SAR数据和LiDAR数据的变化检测也得到了学者们的关注。</p>
<p>变化检测的分类体系：</p>
<img src="https://z3.ax1x.com/2021/04/21/cHjmB6.jpg" style="zoom:33%;" />
<p>变化检测方法发展的时间脉络：</p>
<img src="https://z3.ax1x.com/2021/04/21/cHjnHK.jpg" style="zoom:33%;" />
<h2 id="传统变化检测方法"><a class="markdownIt-Anchor" href="#传统变化检测方法"></a> 传统变化检测方法</h2>
<h3 id="直接比较法"><a class="markdownIt-Anchor" href="#直接比较法"></a> 直接比较法</h3>
<p>直接比较法是不经过分类, 而直接对同一区域不同时相遥感影像的光谱信息进行处理比较, 进而 确定变化的位置与范围, 然后通过人工目视解译或 分类确定变化的类型。目前常用的直接比较法主要<strong>有影像代数法、影像回归法、假彩色合成法、光谱特征变异法 、交叉相关分析法、变化矢量分析法等</strong>。这些方法的优点是直接确定变化的位置, 避免大范围分类, 提高了检测效率, 缺点是不能提供变化的类型。</p>
<p><strong>影像代数法</strong>包括影像差值法与影像比较法。影像差值法（或比值法）将两个时相遥感图像的对应波段相减(或相除) 。其原理是图像中未发生变化的遥感图像上一般具有相等或相近的灰度值，变化时则灰度差别较大。</p>
<ul>
<li>优点：简单快速</li>
<li>缺点：变化阈值难以确定，由于是点对点运算所以一般差值具有很大噪声。</li>
</ul>
<p><strong>影响回归法</strong>：假定 T1 时相的像元值是 T2时相像元值的一个线性函数, 通过最小二乘法来进行回归, 然后用回归方程计算出的预测值减去 T1 时相的原始像元值, 从而获得两时相的回归残差图像。通过设定阈值来确定变化区域。</p>
<h3 id="图像变换类方法"><a class="markdownIt-Anchor" href="#图像变换类方法"></a> 图像变换类方法</h3>
<p><strong>主成分分析法</strong>将不同时相遥感影像进行主成分变换，以压缩波段之间的相关信息，生成互不相关的多时相主分量合成图像，然后对主分量信息进行对比。比较方式有</p>
<ol>
<li><strong>主成分差异法</strong>：对两个时相的影像分别进行 PCA 变换, 选择主要的 几个主成分计算他们之间的差值来检测变化。</li>
<li><strong>差异主成分法</strong>：即先对两时相影像做差值处理, 然后对差值影像进行 PCA 变换, 取一个或几个主要的分量进行变化检测。</li>
<li><strong>多波段主成分变换法</strong>, 即将两时相影像的各个波段组合成一个新的混合影像, 对这个混合影像进行PCA变换, <em>前几个主要分量体现的是不变的信息</em>, 而<em>发生变化的信息将会集中在后几个次要分量中</em>, 因此<strong>对后几个分量进行分析</strong>就可以检测出变化信息。</li>
</ol>
<p>操作方式：为了对图像数据进行 PCA 变换，图像需要转换成一维向量表示。可以使用NumPy 类库中的 flatten() 方法进行变换。将变平的图像堆积起来，我们可以得到一个矩阵，矩阵的一行表示一幅图像。在计算主方向之前，所有的行图像按照平均图像进行了中心化。我们通常使用 SVD（SingularValue Decomposition，奇异值分解）方法来计算主成分。</p>
<p><strong>变化矢量分析法</strong>( Change Vecto r Analy sis, 简称 CVA) 是通过描述从 T1 时相到 T2 时相光谱向量变化的方向和大小来检测变化的一种方法。首先对两时相的影像分别做 KT 变换, 取变换结果的第一和第二分量, 根据影像转换的经验系数对上面的两对分量做旋转变换以使结果分别对应两时相的绿度( G) 和亮度( B) 值, 然后在G, B 坐标系中, 分别计算变化矢量的方向分量( Saturation) 和幅度分量 ( Hue) , 进而通过设定阈值检测变化。</p>
<h3 id="分类后比较法"><a class="markdownIt-Anchor" href="#分类后比较法"></a> 分类后比较法</h3>
<p>分类后比较法是一种较为简单明晰的变化发现方法。首先运用统一的分类体系对每一时相遥感影像单独进行分类, 然后通过对分类结果的比较直接发现变化。 该方法经单独分类后比较, 可以直接获取变化的类型、数量和位置, 对研究区的土地覆盖变化不需要有先验认识；而且能回避所用多时相数据因获取季节不同和传感器不同所带来的归一化问题;另外, 因为它是单独分类, 无时相数的限制, 因此分类后比 较法可以同时进行两个时相以上的遥感影像的变化 检测分析。但分类后比较法一直被认为存在一些较严重的缺陷。首先, 这种对不同时期土地覆盖分类 数据的比较, 无法检测出存在某一种土地覆盖类型内部的细微变化;再者, 两个时相分类数据进行比较 后生成的变化图, 其精度只大致相当于每个时相分类精度值的乘积, 这是因为存在于每一单独分类中 的误差会在空间比较过程中被进一步放大。尽管分类后比较法存在精度方面的缺陷, 但由于其方法简单, 故仍然被经常使用。</p>
<h2 id="对象级变化检测"><a class="markdownIt-Anchor" href="#对象级变化检测"></a> 对象级变化检测</h2>
<p>面向对象的遥感影像分类技术是针对高分辨率影像应用而兴起的一种新的遥感分类技术,可以实现对多源遥感数据或遥感数据和矢量数据的整合分析。基本原理是根据像元的形状、颜色、纹理等特征,把具有相同特征的象素组成一个对象,然后根据每一个对象的特征进行分类。它不同于传统遥感影像分析软件基于像元光谱值的分类方法,而采用决策支持的模糊分类算法,建立不同尺度的分类层次,在每一层次上分别定义对象的光谱特征均值、方差、灰度比值等、形状特征面积、长度、宽度、边界长度、长宽比、形状因子、位置等、纹理特征对象方差、对称性、灰度共生矩阵特征等、上下文关系特征和相邻关系特征,通过对影像对象定义多种特征并指定模糊化函数,给出每个对象隶<br />
属于某一类的概率,建立分类标准,最终按照最大概率产生确定分类结果。</p>
<h2 id="基于深度学习的变化检测"><a class="markdownIt-Anchor" href="#基于深度学习的变化检测"></a> 基于深度学习的变化检测</h2>
<h3 id="autoencoder"><a class="markdownIt-Anchor" href="#autoencoder"></a> Autoencoder</h3>
<h4 id="stacked-denoising-aes"><a class="markdownIt-Anchor" href="#stacked-denoising-aes"></a> stacked denoising AEs</h4>
<blockquote>
<p>Zhang, Puzhao, et al. “Change  detection based on deep feature representation and mapping  transformation for multi-spatial-resolution remote sensing images.” <em>ISPRS Journal of Photogrammetry and Remote Sensing</em> 116 (2016): 24-41.</p>
<p>cited times: 159</p>
</blockquote>
<img src="https://z3.ax1x.com/2021/04/21/cHjdUS.jpg" style="zoom:40%;" />
<p>关于异构图像的change detection问题，提出了基于autoencoder的解决方案。首先使用SRCNN对图像对中的低分辨图像进行超分辨重建以获得更多细节。后用SDAE（stacked denoising  autoencoders ）学习特征。AE, DAE, SDAE的结构如下图所示，多个堆叠在一起的ADE就被称为SDAE，最右是一个2层SDAE的例子。</p>
<p><img src="https://z3.ax1x.com/2021/04/21/cHjw4g.jpg" alt="" /></p>
<p>送入SDAE的是图像中每个元素的灰度邻域特征NGI(neighborhood gray information ), 对一层DAE有：</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mi>F</mi><mrow><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">)</mo></mrow></msup><mo>=</mo><mo stretchy="false">{</mo><msup><mover accent="true"><mi>f</mi><mo>⃗</mo></mover><mrow><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">(</mo><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo stretchy="false">)</mo><mi mathvariant="normal">∣</mi><mn>1</mn><mo>⩽</mo><mi>i</mi><mo>⩽</mo><mi>h</mi><mo separator="true">,</mo><mn>1</mn><mo>⩽</mo><mi>j</mi><mo>⩽</mo><mi>w</mi><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">F^{(d)}=\{\vec{f}^{(d)}(i,j)| 1\leqslant i\leqslant h,1\leqslant j\leqslant w\}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.938em;vertical-align:0em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight">d</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.2274399999999999em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord"><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9774399999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em;">f</span></span></span><span style="top:-3.26344em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.06882999999999997em;"><span class="overlay" style="height:0.714em;width:0.471em;"><svg width='0.471em' height='0.714em' style='width:0.471em' viewBox='0 0 471 714' preserveAspectRatio='xMinYMin'><path d='M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5
3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11
10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63
-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1
-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59
H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359
c-16-25.333-24-45-24-59z'/></svg></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em;"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight">d</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">i</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.05724em;">j</span><span class="mclose">)</span><span class="mord">∣</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel amsrm">⩽</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.79619em;vertical-align:-0.13667em;"></span><span class="mord mathdefault">i</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel amsrm">⩽</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault">h</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel amsrm">⩽</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.05724em;">j</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel amsrm">⩽</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.02691em;">w</span><span class="mclose">}</span></span></span></span></span></p>
<p>coarse initial change mask, 即采用某种方法构造的简陋的初级变化掩码，本文采用OBCD*方法来构建coarse ICM, 选择后分类比较(PCC)作为比较方法，并将PCC的结果作为选择可靠训练样本的要求较高的ICM。然后选择coarse ICM中不变的区域作为SDAE的训练样本。（SDAE的输入与输出分别是两张异构图像）</p>
<blockquote>
<p>*：Chen, G., Hay, G.J., Carvalho, L.M., Wulder, M.A., 2012. Object-based change<br />
detection. Int. J. Remote Sens. 33, 4434–4457</p>
</blockquote>
<p>对于相对应的一组异构图像的像素，即<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>I</mi><mi>h</mi></msub><mo stretchy="false">(</mo><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">I_h(i,j)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em;">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">i</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.05724em;">j</span><span class="mclose">)</span></span></span></span>与<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>I</mi><mi>l</mi></msub><mo stretchy="false">(</mo><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">I_l(i,j)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em;">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.01968em;">l</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">i</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.05724em;">j</span><span class="mclose">)</span></span></span></span>（被称为像素对），有其特征对<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mover accent="true"><mrow><msubsup><mi>f</mi><mi>h</mi><mrow><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">)</mo></mrow></msubsup><mo stretchy="false">(</mo><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo stretchy="false">)</mo></mrow><mo>⃗</mo></mover></mrow><annotation encoding="application/x-tex">\vec{f^{(d)}_h(i,j)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.6291079999999998em;vertical-align:-0.3013079999999999em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3277999999999999em;"><span style="top:-3.0447999999999995em;"><span class="pstrut" style="height:3.0448em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em;"><span style="top:-2.3986920000000005em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span><span style="top:-3.2198em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight">d</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3013079999999999em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">i</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.05724em;">j</span><span class="mclose">)</span></span></span><span style="top:-3.6586em;"><span class="pstrut" style="height:3.0448em;"></span><span class="accent-body" style="left:-0.2355em;"><span class="overlay" style="height:0.714em;width:0.471em;"><svg width='0.471em' height='0.714em' style='width:0.471em' viewBox='0 0 471 714' preserveAspectRatio='xMinYMin'><path d='M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5
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3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11
10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63
-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1
-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59
H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359
c-16-25.333-24-45-24-59z'/></svg></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3013079999999999em;"><span></span></span></span></span></span></span></span></span>。在通过SDAE学习到映射<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>f</mi><mrow><mi>m</mi><mi>a</mi><mi>p</mi></mrow></msub><mo>:</mo><mi>s</mi><msubsup><mi>F</mi><mi>h</mi><mrow><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">)</mo></mrow></msubsup><mo>→</mo><mi>s</mi><msubsup><mi>F</mi><mi>l</mi><mrow><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">)</mo></mrow></msubsup></mrow><annotation encoding="application/x-tex">f_{map}: sF_h^{(d)} \rightarrow sF_l^{(d)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">m</span><span class="mord mathdefault mtight">a</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.3461079999999999em;vertical-align:-0.30130799999999996em;"></span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em;"><span style="top:-2.398692em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span><span style="top:-3.2197999999999998em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight">d</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.30130799999999996em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.3461079999999999em;vertical-align:-0.30130799999999996em;"></span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em;"><span style="top:-2.398692em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.01968em;">l</span></span></span><span style="top:-3.2197999999999998em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight">d</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.30130799999999996em;"><span></span></span></span></span></span></span></span></span></span>后，可以生成最终变化图<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>s</mi><msup><mi>F</mi><mrow><mo stretchy="false">(</mo><mi>d</mi><msub><mo stretchy="false">)</mo><mi>h</mi></msub></mrow></msup></mrow><annotation encoding="application/x-tex">sF^{(d)_h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8879999999999999em;vertical-align:0em;"></span><span class="mord mathdefault">s</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8879999999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight">d</span><span class="mclose mtight"><span class="mclose mtight">)</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">h</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>与<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>s</mi><mover accent="true"><msubsup><mi>F</mi><mi>h</mi><mrow><mo stretchy="false">(</mo><mi>d</mi><mo stretchy="false">)</mo></mrow></msubsup><mo>^</mo></mover></mrow><annotation encoding="application/x-tex">s\hat{F_h^{(d)}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.6095479999999998em;vertical-align:-0.3013079999999999em;"></span><span class="mord mathdefault">s</span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3082399999999998em;"><span style="top:-3.0447999999999995em;"><span class="pstrut" style="height:3.0448em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em;"><span style="top:-2.3986920000000005em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">h</span></span></span><span style="top:-3.2198em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight">d</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3013079999999999em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.6586em;"><span class="pstrut" style="height:3.0448em;"></span><span class="accent-body" style="left:-0.25em;">^</span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3013079999999999em;"><span></span></span></span></span></span></span></span></span>之差，不过定义形式不是相减，而是计算对应元素之间的相似度用来衡量相似程度，即：</p>
<p class='katex-block katex-error' title='ParseError: KaTeX parse error: No such environment: align* at position 7: \begin{̲a̲l̲i̲g̲n̲*̲}̲
cd(i,j) &amp;= 1-s…'>\begin{align*}
cd(i,j) &amp;= 1-sim(\hat{F}^{(d)}_h(i,j),F^{(n)}_l(i,j))\\ 
 &amp;= 1-sim(f_{map}(F_h^{(d)}(i,j)),F^{(n)}_l(i,j))
\end{align*}</p>
<p>并得到<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>C</mi><mi>M</mi></mrow><annotation encoding="application/x-tex">CM</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mord mathdefault" style="margin-right:0.10903em;">M</span></span></span></span>：</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>C</mi><mi>M</mi><mo>=</mo><mo stretchy="false">{</mo><mi>c</mi><mi>d</mi><mo stretchy="false">(</mo><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo stretchy="false">)</mo><mi mathvariant="normal">∣</mi><mn>1</mn><mo>⩽</mo><mi>i</mi><mo>⩽</mo><mi>h</mi><mo separator="true">,</mo><mn>1</mn><mo>⩽</mo><mi>j</mi><mo>⩽</mo><mi>w</mi><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">CM=\{cd(i,j)|1\leqslant i\leqslant h, 1\leqslant j\leqslant w\}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mord mathdefault" style="margin-right:0.10903em;">M</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord mathdefault">c</span><span class="mord mathdefault">d</span><span class="mopen">(</span><span class="mord mathdefault">i</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.05724em;">j</span><span class="mclose">)</span><span class="mord">∣</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel amsrm">⩽</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.79619em;vertical-align:-0.13667em;"></span><span class="mord mathdefault">i</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel amsrm">⩽</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault">h</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel amsrm">⩽</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.05724em;">j</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel amsrm">⩽</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.02691em;">w</span><span class="mclose">}</span></span></span></span></span></p>
<p>然后用聚类的方法（本文采用Fuzzy local information C-means）来对CM进行聚类。</p>
<h4 id="daepropose-sccn"><a class="markdownIt-Anchor" href="#daepropose-sccn"></a> DAE(propose SCCN):</h4>
<blockquote>
<p>Liu, Jia, et al. “A deep convolutional coupling network for change detection based on heterogeneous optical and radar images.” <em>IEEE transactions on neural networks and learning systems</em> 29.3 (2016): 545-559.</p>
<p>cited times: 159</p>
</blockquote>
<p>提出了SCCN网络结构，描述如下：</p>
<p>因为目标是估计像素级的差异而不是区域差异，所以这里不使用池化层。耦合层的任何特征图中的每个像素都使用相同的连接权值集来减少网络参数的总数。这相当于1×1卷积内核的输入特征映射。虽然SCCN按照其原始定义是对称的，但为了适应两张输入图像的不同性质，允许网络两边的耦合层数不同。差分图是通过计算<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">H_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>和<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>H</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">H_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.08125em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>之间的像素距离生成的：</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>D</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>=</mo><mi mathvariant="normal">∣</mi><mi mathvariant="normal">∣</mi><msub><mi>h</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>−</mo><msub><mi>h</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mi mathvariant="normal">∣</mi><msub><mi mathvariant="normal">∣</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">D(x,y)=||h_1(x,y)-h_2(x,y)||_2
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">∣</span><span class="mord">∣</span><span class="mord"><span class="mord mathdefault">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathdefault">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mord">∣</span><span class="mord"><span class="mord">∣</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></p>
<p><strong>学习过程</strong></p>
<p>定义耦合函数：</p>
<p class='katex-block katex-error' title='ParseError: KaTeX parse error: No such environment: align* at position 7: \begin{̲a̲l̲i̲g̲n̲*̲}̲
&amp;min\quad F_{c…'>\begin{align*}
&amp;min\quad F_{cop}(\theta,P_u)=\sum_{(x,y)}P_u(x,y)||h_1(x,y)-h_2(x,y)||_2-\lambda \sum_{(x,y)}P_u(x,y)\\
&amp; s.t.\quad 0\leqslant P_u(x,y)\leqslant 1 
\end{align*}</p>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>θ</mi></mrow><annotation encoding="application/x-tex">\theta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">θ</span></span></span></span>是卷积层与耦合层的各种参数，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>P</mi><mi>u</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P_u(x,y)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">u</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mclose">)</span></span></span></span>是像素点<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(x,y)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mclose">)</span></span></span></span>不发生改变的概率，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>−</mo><mi>λ</mi><msub><mo>∑</mo><mrow><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo></mrow></msub><msub><mi>P</mi><mi>u</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">-\lambda \sum_{(x,y)}P_u(x,y)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.22471em;vertical-align:-0.47471em;"></span><span class="mord">−</span><span class="mord mathdefault">λ</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.22528999999999993em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathdefault mtight" style="margin-right:0.03588em;">y</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.47471em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">u</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mclose">)</span></span></span></span> 是正则化项防止0概率的产生。</p>
<p>算法流程：</p>
<ol>
<li>Initialization: randomly initializing <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>P</mi><mi>u</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>=</mo><mi>r</mi><mi>a</mi><mi>n</mi><mi>d</mi><mo stretchy="false">(</mo><mn>0</mn><mo separator="true">,</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P_u(x,y)=rand(0,1)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">u</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">r</span><span class="mord mathdefault">a</span><span class="mord mathdefault">n</span><span class="mord mathdefault">d</span><span class="mopen">(</span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">1</span><span class="mclose">)</span></span></span></span></li>
<li>updating $$\theta$$: minimizing the objective function <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>F</mi><mrow><mi>c</mi><mi>o</mi><mi>p</mi></mrow></msub><mo stretchy="false">(</mo><mi>θ</mi><mo separator="true">,</mo><msub><mi>P</mi><mi>u</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F_{cop}(\theta,P_u)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">c</span><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">p</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">θ</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">u</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></li>
<li>updating <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>P</mi><mi>U</mi></msub></mrow><annotation encoding="application/x-tex">P_U</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.10903em;">U</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></li>
<li>Repetition: repeating steps 2 and 3 until the value of the<br />
objective function in is unchanged.</li>
</ol>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>P</mi><mi>u</mi></msub></mrow><annotation encoding="application/x-tex">P_u</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">u</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>的更新公式：</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>P</mi><mi>u</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mn>1</mn><mspace width="1em"/><mi mathvariant="normal">∣</mi><mi mathvariant="normal">∣</mi><msub><mi>h</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>−</mo><msub><mi>h</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mi mathvariant="normal">∣</mi><msub><mi mathvariant="normal">∣</mi><mn>2</mn></msub><mo>&lt;</mo><mi>λ</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mn>0</mn><mspace width="1em"/><mi mathvariant="normal">∣</mi><mi mathvariant="normal">∣</mi><msub><mi>h</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>−</mo><msub><mi>h</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mi mathvariant="normal">∣</mi><msub><mi mathvariant="normal">∣</mi><mn>2</mn></msub><mo>⩾</mo><mi>λ</mi></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">P_u(x,y)=\left\{\begin{matrix}
1\quad ||h_1(x,y)-h_2(x,y)||_2 &lt; \lambda\\ 
0\quad ||h_1(x,y)-h_2(x,y)||_2 \geqslant  \lambda
\end{matrix}\right.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">u</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">{</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:1em;"></span><span class="mord">∣</span><span class="mord">∣</span><span class="mord"><span class="mord mathdefault">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathdefault">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mord">∣</span><span class="mord"><span class="mord">∣</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">λ</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0</span><span class="mspace" style="margin-right:1em;"></span><span class="mord">∣</span><span class="mord">∣</span><span class="mord"><span class="mord mathdefault">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathdefault">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mord">∣</span><span class="mord"><span class="mord">∣</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel amsrm">⩾</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">λ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<p>但这种算法会导致退化问题，i.e. <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>h</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>≡</mo><msub><mi>h</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">h_1(x,y)\equiv h_2(x,y)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathdefault">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≡</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathdefault">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mclose">)</span></span></span></span>，为解决这个问题，对SCCN的每一边应用DAE。这样SCCN其中一侧的参数由DAE固定，另一侧的参数则有上述算法学习得到。应用于SAR的DAE和应用于光学图像的DAE分别施加伽马噪声与高斯噪声来实施corrupt的过程。</p>
<p><img src="https://z3.ax1x.com/2021/04/21/cHjBCQ.jpg" alt="" /></p>
<h3 id="deep-belief-network"><a class="markdownIt-Anchor" href="#deep-belief-network"></a> Deep belief Network</h3>
<h4 id="rbm"><a class="markdownIt-Anchor" href="#rbm"></a> RBM:</h4>
<blockquote>
<p>Gong, Maoguo, et al. “Change detection in synthetic aperture radar images based on deep neural networks.” <em>IEEE transactions on neural networks and learning systems</em> 27.1 (2015): 125-138.</p>
<p>cited times: 319</p>
</blockquote>
<p>采用的是RBM网络（受限玻尔兹曼机）。指导方针是用训练好的深度神经网络直接从两幅图像中生成变化检测图（change detection map），该方法可以省略生成差分图像的过程。</p>
<ol>
<li>预先分类，获取一些具有较高精度标签的数据;</li>
<li>构建深度神经网络，学习图像特征，然后微调神经网络参数;</li>
<li>利用训练好的深度神经网络对变化像素和不变像素进行分类。</li>
</ol>
<p><strong>the change of procedure</strong></p>
<p>该文章提出了基于深度学习的检测方法的框架（图b），区别于传统检测方法（图a）</p>
<img src="https://z3.ax1x.com/2021/04/21/cHjD3j.jpg" style="zoom:50%;" />
<p>flowchart:</p>
<img src="https://z3.ax1x.com/2021/04/21/cHjsvn.jpg" style="zoom:33%;" />
<p><strong>procedure</strong></p>
<ol>
<li>用FCM逐像素点的确定变化与未变化区域。未改变的信息有相同的标签，改变的信息有不同的标签。这是预分类与数据生成的部分。预分类的结果并不完全正确。选择被正确分类概率高的像素来训练网络。</li>
<li>搭建神经网络，输入的为某一点的邻域，将两张图像的对于对应像素点的矩阵flatten再connect，放入RBM（受限玻尔兹曼机）</li>
<li>网络输出像素的类标签。类标号0表示被改变的像素，类标号1表示像素不变。</li>
</ol>
<h4 id="dbn"><a class="markdownIt-Anchor" href="#dbn"></a> DBN:</h4>
<blockquote>
<p>Zhang, Hui, et al. “Feature-level change detection using deep  representation and feature change analysis for multispectral imagery.” <em>IEEE Geoscience and Remote Sensing Letters</em> 13.11 (2016): 1666-1670.</p>
<p>cited times: 69</p>
</blockquote>
<p><em>深度信念网络（Deep Belief Network，DBN）是一种深层的概率有向图模型，其图结构由多层的节点构成。每层节点的内部没有连接，相邻两层的节点之间为全连接。网络的最底层为可观测变量，其他层节点都为隐变量。深度信念网络是一个生成模型，可以用来生成符合特定分布的样本。隐变量用来描述在可观测变量之间的高阶相关性。</em></p>
<p><img src="https://z3.ax1x.com/2021/04/21/cHjcD0.jpg" alt="" /></p>
<p>对于DBN得到的特征向量<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>V</mi><mrow><mi>t</mi><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">V_{t1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">t</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>与<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>V</mi><mrow><mi>t</mi><mn>2</mn></mrow></msub></mrow><annotation encoding="application/x-tex">V_{t2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">t</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>，计算余弦相似度的模：</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>p</mi><mo>=</mo><mn>1</mn><mo>−</mo><mfrac><mrow><msub><mi>V</mi><mrow><mi>t</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><msub><mi>V</mi><mrow><mi>t</mi><mn>2</mn></mrow></msub><msup><mo stretchy="false">)</mo><mo mathvariant="normal">′</mo></msup></mrow><mrow><msqrt><mrow><msub><mi>V</mi><mrow><mi>t</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><msub><mi>V</mi><mrow><mi>t</mi><mn>1</mn></mrow></msub><msup><mo stretchy="false">)</mo><mo mathvariant="normal">′</mo></msup></mrow></msqrt><msqrt><mrow><msub><mi>V</mi><mrow><mi>t</mi><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><msub><mi>V</mi><mrow><mi>t</mi><mn>2</mn></mrow></msub><msup><mo stretchy="false">)</mo><mo mathvariant="normal">′</mo></msup></mrow></msqrt></mrow></mfrac></mrow><annotation encoding="application/x-tex">p=1-\frac{V_{t1}(V_{t2})&#x27;}{\sqrt{V_{t1}(V_{t1})&#x27;}\sqrt{V_{t2}(V_{t2})&#x27;}}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathdefault">p</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.558892em;vertical-align:-1.13em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.428892em;"><span style="top:-2.175em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.935em;"><span class="svg-align" style="top:-3.2em;"><span class="pstrut" style="height:3.2em;"></span><span class="mord" style="padding-left:1em;"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">t</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">t</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6778919999999999em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span><span style="top:-2.8950000000000005em;"><span class="pstrut" style="height:3.2em;"></span><span class="hide-tail" style="min-width:1.02em;height:1.28em;"><svg width='400em' height='1.28em' viewBox='0 0 400000 1296' preserveAspectRatio='xMinYMin slice'><path d='M263,681c0.7,0,18,39.7,52,119c34,79.3,68.167,
158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067
c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84,
175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71
c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3,
-252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26
s76,-59,76,-59s76,-60,76,-60z M1001 80H40000v40H1012z'/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.30499999999999994em;"><span></span></span></span></span></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.935em;"><span class="svg-align" style="top:-3.2em;"><span class="pstrut" style="height:3.2em;"></span><span class="mord" style="padding-left:1em;"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">t</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">t</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6778919999999999em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span><span style="top:-2.8950000000000005em;"><span class="pstrut" style="height:3.2em;"></span><span class="hide-tail" style="min-width:1.02em;height:1.28em;"><svg width='400em' height='1.28em' viewBox='0 0 400000 1296' preserveAspectRatio='xMinYMin slice'><path d='M263,681c0.7,0,18,39.7,52,119c34,79.3,68.167,
158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067
c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84,
175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71
c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3,
-252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26
s76,-59,76,-59s76,-60,76,-60z M1001 80H40000v40H1012z'/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.30499999999999994em;"><span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">t</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">t</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.751892em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.13em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<p>以及其方向：</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>V</mi><mi>D</mi></msub><mo>=</mo><msub><mi>V</mi><mn>2</mn></msub><mo>−</mo><msub><mi>V</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">V_D=V_2-V_1
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.02778em;">D</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>θ</mi><mo>=</mo><mi>a</mi><mi>r</mi><mi>c</mi><mi>c</mi><mi>o</mi><mi>s</mi><mo stretchy="false">[</mo><mfrac><mn>1</mn><msqrt><mi>N</mi></msqrt></mfrac><mo stretchy="false">(</mo><mfrac><mrow><munderover><mo>∑</mo><mrow><mi>b</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msub><mi>V</mi><mrow><mi>b</mi><mo separator="true">,</mo><mi>D</mi></mrow></msub></mrow><msqrt><mrow><munderover><mo>∑</mo><mrow><mi>b</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msubsup><mi>V</mi><mrow><mi>b</mi><mo separator="true">,</mo><mi>D</mi></mrow><mn>2</mn></msubsup></mrow></msqrt></mfrac><mo stretchy="false">)</mo><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">\theta = arccos[\frac{1}{\sqrt{N}}(\frac{\sum^N_{b=1}V_{b,D}}{\sqrt{\sum^N_{b=1}V_{b,D}^2}})]
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">θ</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.400941em;vertical-align:-1.73em;"></span><span class="mord mathdefault">a</span><span class="mord mathdefault" style="margin-right:0.02778em;">r</span><span class="mord mathdefault">c</span><span class="mord mathdefault">c</span><span class="mord mathdefault">o</span><span class="mord mathdefault">s</span><span class="mopen">[</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.1833349999999996em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9266650000000001em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord mathdefault" style="margin-right:0.10903em;">N</span></span></span><span style="top:-2.886665em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,
-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,
-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,
35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,
-221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467
s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422
s-65,47,-65,47z M834 80H400000v40H845z'/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.11333499999999996em;"><span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.93em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mopen">(</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.670941em;"><span style="top:-2.11em;"><span class="pstrut" style="height:3.2569075em;"></span><span class="mord"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2569075em;"><span class="svg-align" style="top:-3.8em;"><span class="pstrut" style="height:3.8em;"></span><span class="mord" style="padding-left:1em;"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.981231em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">b</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.795908em;"><span style="top:-2.3986920000000005em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">b</span><span class="mpunct mtight">,</span><span class="mord mathdefault mtight" style="margin-right:0.02778em;">D</span></span></span></span><span style="top:-3.0448000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4374159999999999em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.2169075em;"><span class="pstrut" style="height:3.8em;"></span><span class="hide-tail" style="min-width:1.02em;height:1.8800000000000001em;"><svg width='400em' height='1.8800000000000001em' viewBox='0 0 400000 1944' preserveAspectRatio='xMinYMin slice'><path d='M1001,80H400000v40H1013.1s-83.4,268,-264.1,840c-180.7,
572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7s-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,
-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744c-10,12,-21,25,-33,39s-32,39,-32,39
c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30c26.7,-32.7,52,-63,76,-91s52,-60,52,-60
s208,722,208,722c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,
-658.5c53.7,-170.3,84.5,-266.8,92.5,-289.5c4,-6.7,10,-10,18,-10z
M1001 80H400000v40H1013z'/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5830924999999999em;"><span></span></span></span></span></span></span></span><span style="top:-3.4869075em;"><span class="pstrut" style="height:3.2569075em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.9466175000000003em;"><span class="pstrut" style="height:3.2569075em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.981231em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">b</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">b</span><span class="mpunct mtight">,</span><span class="mord mathdefault mtight" style="margin-right:0.02778em;">D</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.73em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose">)</span><span class="mclose">]</span></span></span></span></span></p>
<p>根据特征变化矢量的大小ρ和方向θ，可以将变化信息压缩到二维极坐标域中。首先，利用广泛应用的无监督聚类技术FLICM，对变化幅度ρ进行变化和不变像素的区分。然后，根据变化方向θ，将变化的像素聚类为几种不同的变化类型。</p>
<h3 id="cnn"><a class="markdownIt-Anchor" href="#cnn"></a> CNN</h3>
<blockquote>
<p>Sakurada, Ken, and Takayuki Okatani.  “Change Detection from a Street Image Pair using CNN Features and  Superpixel Segmentation.” <em>BMVC</em>. Vol. 61. 2015.</p>
<p>cited times:  73  2015年的，文章长度较短，非卫星图像变化检测，而是街景变化检测</p>
</blockquote>
<p>略</p>
<h4 id="pca-net"><a class="markdownIt-Anchor" href="#pca-net"></a> PCA-Net</h4>
<blockquote>
<p>Gao, Feng, et al. “Automatic change detection in synthetic aperture radar images based on PCANet.” <em>IEEE Geoscience and Remote Sensing Letters</em> 13.12 (2016): 1792-1796.</p>
<p>cited times: 86   PCANet</p>
</blockquote>
<p><strong>How does PCANet works?</strong></p>
<p><img src="https://z3.ax1x.com/2021/04/21/cHjRET.jpg" alt="" /></p>
<p>因此可以看出PCANet是作为一种特征提取器的存在。本文将PCANet应用于change detection的主要流程为：</p>
<ol>
<li>使用log-ratio算子对图像进行变换后利用Gabor小波和FCM算法对有较大概率发生变化或不变的兴趣点进行选择。（对log-ratio图进行Gabor特征提取，然后使用FCM算法聚类得到预分类图像）</li>
<li>生成以感兴趣像素为中心的图像patch。PCANet模型使用这些patch进行训练。</li>
<li>第1步中的剩余像素使用经过训练的PCANet模型进一步划分为变化和不变类。然后，将PCANet分类结果与预分类结果相结合，形成最终的变化图。</li>
</ol>
<p>然后将PCANet提取的特征输入线性支持向量机训练模型。使用这个模型，像素被进一步分离成改变的和没有改变的类。最后，将PCANet分类结果与预分类结果结合，形成最终的变化图。</p>
<h4 id="region-cnn"><a class="markdownIt-Anchor" href="#region-cnn"></a> Region-CNN</h4>
<blockquote>
<p>Khan, Salman H., et al. “Forest change detection in incomplete satellite images with deep neural networks.” <em>IEEE Transactions on Geoscience and Remote Sensing</em> 55.9 (2017): 5407-5423.</p>
<p>cited times: 76   Region-CNN</p>
</blockquote>
<p>前面讲述了许多与遥感图像处理相关的技术（去噪，去云层等），不做探究。网络结构部分充分借鉴了R-CNN的思维，在一张图上生成多个尺度的region，并且通过计算 IoU指标，采取非极大性抑制，以最高分的区域为基础，剔除掉那些重叠位置的区域。将一系列region送入网络，region被标注为变化或者未变化。</p>
<p><img src="https://z3.ax1x.com/2021/04/21/cHj4C4.jpg" alt="" /></p>
<h4 id="unet"><a class="markdownIt-Anchor" href="#unet"></a> UNet++</h4>
<blockquote>
<p>Peng, Daifeng, Yongjun Zhang, and  Haiyan Guan. “End-to-end change detection for high resolution satellite  images using improved UNet++.” <em>Remote Sensing</em> 11.11 (2019): 1382.</p>
<p>cited times:  76   使用的UNet++</p>
</blockquote>
<p>概述：现有的基于深度学习的change detection大多是通过利用深度特征生成差分图像或学习像素块之间的变化关系来实现的，这导致了错误积累的问题，因为需要许多中间处理步骤才能获得最终的变化图。为了解决上述问题，提出了一种基于UNet<ins>的有效encoder-decoder结构的端到端语义分割方法，该方法可以利用已有的标注数据集从头开始学习变化图。首先，将共配准图像对进行连接作为改进的UNet</ins>网络的输入，利用全局和细粒度信息生成具有较高空间精度的特征地图。然后，采用多边输出融合策略，将不同语义层次的变化图进行融合，从而生成高精度的最终变化图。</p>
<p><em>在基础的分类任务中，标准CNN架构中的最后几层总是几个全连接(FC)层，以一维分布的所有类作为输出。然而，对于语义分割任务，需要一个二维密集类预测图。在标准CNN的基础上，提出了一种基于patch的CNN方法，其中每个像素的标签由包围它的patch生成。其次有用于语义分割的FCN，去掉FC层，用卷积层代替。在FCN中，输入图像经过多次卷积和池化运算后向下采样为小图像，然后通过双线性插值或反卷积将向下采样的图像向上采样为原始图像大小。由于计算在重叠区域之间共享，FCN获得了很高的效率。</em></p>
<p>而Encoder-Decoder在语义分割领域如今十分流行。本文基于UNet<ins>实现change detection任务。UNet</ins>的不同层中采用dense connection。</p>
<p>feature map 可以表示为：</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mi>x</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi></mrow></msup><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>H</mi><mo stretchy="false">(</mo><msup><mi>x</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn><mo separator="true">,</mo><mi>j</mi></mrow></msup><mo stretchy="false">)</mo><mspace width="1em"/><mi>j</mi><mo>=</mo><mn>0</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>H</mi><mo stretchy="false">(</mo><mo stretchy="false">[</mo><mo stretchy="false">[</mo><msup><mi>x</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>k</mi></mrow></msup><msubsup><mo stretchy="false">]</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>j</mi><mo>−</mo><mn>1</mn></mrow></msubsup><mo separator="true">,</mo><mo stretchy="false">(</mo><msup><mi>x</mi><mrow><mi>i</mi><mo>+</mo><mn>1</mn><mo separator="true">,</mo><mi>j</mi><mo>−</mo><mn>1</mn></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo stretchy="false">)</mo><mspace width="1em"/><mi>j</mi><mo>&gt;</mo><mn>0</mn></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">x^{i,j}=\left\{\begin{matrix}
H(x^{i-1,j}) \quad j=0\\ 
H([[x^{i,k}]^{j-1}_{k=0},(x^{i+1,j-1})]) \quad j&gt;0
\end{matrix}\right.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.874664em;vertical-align:0em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.874664em;"><span style="top:-3.1130000000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathdefault mtight" style="margin-right:0.05724em;">j</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.5025720000000007em;vertical-align:-1.0012860000000006em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">{</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5012860000000001em;"><span style="top:-3.661286em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.824664em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathdefault mtight" style="margin-right:0.05724em;">j</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathdefault" style="margin-right:0.05724em;">j</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord">0</span></span></span><span style="top:-2.3587139999999995em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="mopen">(</span><span class="mopen">[</span><span class="mopen">[</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathdefault mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span></span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.942572em;"><span style="top:-2.3986920000000005em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.1809080000000005em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em;">j</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3013079999999999em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.824664em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathdefault mtight" style="margin-right:0.05724em;">j</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mclose">]</span><span class="mclose">)</span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathdefault" style="margin-right:0.05724em;">j</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.0012860000000006em;"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>H</mi><mo stretchy="false">(</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">H()</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="mopen">(</span><span class="mclose">)</span></span></span></span>表示卷积运算与激活函数，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo stretchy="false">(</mo><mo>⋅</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(\cdot)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">⋅</span><span class="mclose">)</span></span></span></span>指上采样操作，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo stretchy="false">[</mo><mo>⋅</mo><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[\cdot]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord">⋅</span><span class="mclose">]</span></span></span></span>指连接操作。</p>
<img src="https://z3.ax1x.com/2021/04/21/cHjI29.jpg" style="zoom:33%;" />
<h3 id="lstm"><a class="markdownIt-Anchor" href="#lstm"></a> LSTM</h3>
<h4 id="improved-lstm"><a class="markdownIt-Anchor" href="#improved-lstm"></a> improved LSTM</h4>
<blockquote>
<p>Lyu, Haobo, Hui Lu, and Lichao Mou.  “Learning a transferable change rule from a recurrent neural network for land cover change detection.” <em>Remote Sensing</em> 8.6 (2016): 506.</p>
<p>cited times:179</p>
</blockquote>
<p>输入：多时相图像对<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mi>X</mi><msub><mi>T</mi><mn>1</mn></msub></msup></mrow><annotation encoding="application/x-tex">X^{T_1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8413309999999999em;vertical-align:0em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mi>X</mi><msub><mi>T</mi><mn>2</mn></msub></msup></mrow><annotation encoding="application/x-tex">X^{T_2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8413309999999999em;vertical-align:0em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>。对于每一个像素都有对应标签<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>Y</mi><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>0</mn><mo separator="true">,</mo><mn>1</mn><mo stretchy="false">)</mo><mo separator="true">,</mo><mo stretchy="false">(</mo><mn>1</mn><mo separator="true">,</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></mrow><annotation encoding="application/x-tex">Y={(0,1),(1,0)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mopen">(</span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">0</span><span class="mclose">)</span></span></span></span></span>，前一个元素表示像素未变化，后一个表示已变化。（对于多分类变化检测，则可以使用one-hot编码）</p>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msubsup><mi mathvariant="bold">x</mi><mi>i</mi><msub><mi>T</mi><mn>1</mn></msub></msubsup></mrow><annotation encoding="application/x-tex">\mathbf{x}_i^{T_1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.200095em;vertical-align:-0.276864em;"></span><span class="mord"><span class="mord"><span class="mord mathbf">x</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9232309999999999em;"><span style="top:-2.4231360000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.1449000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em;"><span></span></span></span></span></span></span></span></span></span>与<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msubsup><mi mathvariant="bold">x</mi><mi>i</mi><msub><mi>T</mi><mn>2</mn></msub></msubsup></mrow><annotation encoding="application/x-tex">\mathbf{x}_i^{T_2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.200095em;vertical-align:-0.276864em;"></span><span class="mord"><span class="mord"><span class="mord mathbf">x</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9232309999999999em;"><span style="top:-2.4231360000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.1449000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.276864em;"><span></span></span></span></span></span></span></span></span></span>是多时相图像对<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mi>X</mi><mrow><mi>T</mi><mn>1</mn></mrow></msup></mrow><annotation encoding="application/x-tex">X^{T1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8413309999999999em;vertical-align:0em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span></span></span>，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mi>X</mi><mrow><mi>T</mi><mn>2</mn></mrow></msup></mrow><annotation encoding="application/x-tex">X^{T2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8413309999999999em;vertical-align:0em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span> 的像素，则基于LSTM建模概率分布<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>p</mi><mo stretchy="false">(</mo><msub><mi>y</mi><mi>i</mi></msub><mi mathvariant="normal">∣</mi><msubsup><mi>x</mi><mi>i</mi><mrow><mi>T</mi><mn>1</mn></mrow></msubsup><mo separator="true">,</mo><msubsup><mi>x</mi><mi>i</mi><mrow><mi>T</mi><mn>2</mn></mrow></msubsup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">p(y_i|x_i^{T1},x_i^{T2})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0999949999999998em;vertical-align:-0.258664em;"></span><span class="mord mathdefault">p</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">∣</span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-2.441336em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-2.441336em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.258664em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span>。</p>
<blockquote>
<p>一个小思考，如果要建立概率分布，用变分自编码器是否会是一个可行的途径。这里使用LSTM的原因是可以将图像的像素点及其邻域特征逐行输入作为LSTM的时序信息。那么如何将变分自编码器与邻域信息结合？</p>
</blockquote>
<p>流程：</p>
<ol>
<li>将<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>T</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">T_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>的原始像素向量(6个波段)输入到输入层。然后，隐含层(由LSTM单元组成)接收输入并计算当前输入的状态信息；同时，它还恢复那些状态值。</li>
<li>然后，将<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>T</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">T_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>图像对应的像素向量与状态信息同时输入到隐含层，当前隐含层可以学习到两个像素向量之间的变化信息。</li>
<li>最后，裁判模型可以根据隐含层中学习到的变化信息，通过最后一个决策层预测变化或未变化的标记。</li>
</ol>
<p>input node:</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mi>g</mi><mrow><mo stretchy="false">(</mo><msub><mi>T</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></msup><mo>=</mo><mi>ϕ</mi><mo stretchy="false">(</mo><msub><mi mathvariant="bold">W</mi><mrow><mi>g</mi><mi>x</mi></mrow></msub><msup><mi mathvariant="bold">x</mi><msub><mi>T</mi><mn>2</mn></msub></msup><mo>+</mo><msub><mi mathvariant="bold">W</mi><mrow><mi>g</mi><mi>h</mi></mrow></msub><msup><mi mathvariant="bold">h</mi><msub><mi>T</mi><mn>1</mn></msub></msup><mo>+</mo><msub><mi mathvariant="bold">b</mi><mi>g</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">g^{(T_2)}=\phi(\mathbf{W}_{gx}\mathbf{x}^{T_2}+\mathbf{W}_{gh}\mathbf{h}^{T_1}+\mathbf{b}_g)
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.13244em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.177439em;vertical-align:-0.286108em;"></span><span class="mord mathdefault">ϕ</span><span class="mopen">(</span><span class="mord"><span class="mord"><span class="mord mathbf" style="margin-right:0.01597em;">W</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">g</span><span class="mord mathdefault mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">x</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.177439em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord"><span class="mord mathbf" style="margin-right:0.01597em;">W</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">g</span><span class="mord mathdefault mtight">h</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">h</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord"><span class="mord mathbf">b</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">g</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mi mathvariant="bold">h</mi><mrow><mo stretchy="false">(</mo><msub><mi>T</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mrow></msup></mrow><annotation encoding="application/x-tex">\mathbf{h}^{(T_1)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8879999999999999em;vertical-align:0em;"></span><span class="mord"><span class="mord"><span class="mord mathbf">h</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8879999999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span></span></span></span>是hidden layer。<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ϕ</mi></mrow><annotation encoding="application/x-tex">\phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault">ϕ</span></span></span></span>是一种激活函数（并不一定是sigmoid）。</p>
<p>the forward pass of the input gate is:</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mi mathvariant="bold">i</mi><mrow><mo stretchy="false">(</mo><msub><mi>T</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></msup><mo>=</mo><mi>σ</mi><mo stretchy="false">(</mo><msub><mi mathvariant="bold">W</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>x</mi></mrow></msub><msup><mi mathvariant="bold">x</mi><msub><mi>T</mi><mn>2</mn></msub></msup><mo>+</mo><msub><mi mathvariant="bold">W</mi><mrow><mi>i</mi><mi>h</mi></mrow></msub><msup><mi mathvariant="bold">h</mi><msub><mi>T</mi><mn>1</mn></msub></msup><mo>+</mo><msub><mi mathvariant="bold">b</mi><mi>i</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\mathbf{i}^{(T_2)}=\sigma(\mathbf{W}_{i,x}\mathbf{x}^{T_2}+\mathbf{W}_{ih}\mathbf{h}^{T_1}+\mathbf{b}_i)
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.938em;vertical-align:0em;"></span><span class="mord"><span class="mord"><span class="mord mathbf">i</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.177439em;vertical-align:-0.286108em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">σ</span><span class="mopen">(</span><span class="mord"><span class="mord"><span class="mord mathbf" style="margin-right:0.01597em;">W</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathdefault mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">x</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.0413309999999998em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord"><span class="mord mathbf" style="margin-right:0.01597em;">W</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">h</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">h</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord"><span class="mord mathbf">b</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p>
<p>memory cell:</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mi mathvariant="bold">s</mi><msub><mi>T</mi><mn>2</mn></msub></msup><mo>=</mo><msup><mi mathvariant="bold">g</mi><msub><mi>T</mi><mn>2</mn></msub></msup><mo>⊙</mo><msup><mi mathvariant="bold">i</mi><msub><mi>T</mi><mn>2</mn></msub></msup><mo>+</mo><msup><mi mathvariant="bold">s</mi><msub><mi>T</mi><mn>1</mn></msub></msup></mrow><annotation encoding="application/x-tex">\mathbf{s}^{T_2}=\mathbf{g}^{T_2}\odot\mathbf{i}^{T_2}+\mathbf{s}^{T_1}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8913309999999999em;vertical-align:0em;"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.0857709999999998em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord"><span class="mord mathbf" style="margin-right:0.01597em;">g</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⊙</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.9746609999999999em;vertical-align:-0.08333em;"></span><span class="mord"><span class="mord"><span class="mord mathbf">i</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.8913309999999999em;vertical-align:0em;"></span><span class="mord"><span class="mord"><span class="mord mathbf">s</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⊙</mo></mrow><annotation encoding="application/x-tex">\odot</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">⊙</span></span></span></span>表示逐点乘法。</p>
<p>forget gate:</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mi mathvariant="bold">f</mi><mrow><mo stretchy="false">(</mo><msub><mi>T</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></msup><mo>=</mo><mi>σ</mi><mo stretchy="false">(</mo><msub><mi>W</mi><mrow><mi>f</mi><mi>x</mi></mrow></msub><msup><mi mathvariant="bold">x</mi><msub><mi>T</mi><mn>2</mn></msub></msup><mo>+</mo><msub><mi>W</mi><mrow><mi>f</mi><mi>h</mi></mrow></msub><msup><mi mathvariant="bold">h</mi><msub><mi>T</mi><mn>1</mn></msub></msup><mo>+</mo><msub><mi mathvariant="bold">b</mi><mi>f</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\mathbf{f}^{(T_2)}=\sigma(W_{fx}\mathbf{x}^{T_2}+W_{fh}\mathbf{h}^{T_1}+\mathbf{b}_f)
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.938em;vertical-align:0em;"></span><span class="mord"><span class="mord"><span class="mord mathbf" style="margin-right:0.10903em;">f</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.177439em;vertical-align:-0.286108em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">σ</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">W</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em;">f</span><span class="mord mathdefault mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">x</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.177439em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">W</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em;">f</span><span class="mord mathdefault mtight">h</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">h</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord"><span class="mord mathbf">b</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p>
<p>output gate:</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msup><mi mathvariant="bold">o</mi><mrow><mo stretchy="false">(</mo><msub><mi>T</mi><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></msup><mo>=</mo><mi>σ</mi><mo stretchy="false">(</mo><msub><mi mathvariant="bold">W</mi><mrow><mi>o</mi><mi>x</mi></mrow></msub><msup><mi mathvariant="bold">x</mi><msub><mi>T</mi><mn>2</mn></msub></msup><mo>+</mo><msub><mi mathvariant="bold">W</mi><mrow><mi>o</mi><mi>h</mi></mrow></msub><msup><mi mathvariant="bold">h</mi><msub><mi>T</mi><mn>1</mn></msub></msup><mo>+</mo><msub><mi mathvariant="bold">b</mi><mi>o</mi></msub></mrow><annotation encoding="application/x-tex">\mathbf{o}^{(T_2)}=\sigma(\mathbf{W}_{ox}\mathbf{x}^{T_2}+\mathbf{W}_{oh}\mathbf{h}^{T_1}+\mathbf{b}_o
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.938em;vertical-align:0em;"></span><span class="mord"><span class="mord"><span class="mord mathbf">o</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.1413309999999999em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">σ</span><span class="mopen">(</span><span class="mord"><span class="mord"><span class="mord mathbf" style="margin-right:0.01597em;">W</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">x</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.0413309999999998em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord"><span class="mord mathbf" style="margin-right:0.01597em;">W</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">h</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathbf">h</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord"><span class="mord mathbf">b</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">o</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></p>
<p>此外，在该模型中还加入了peephole connections。该部件可以从内部状态直接传递到输入、输出和遗忘门。因为第一阶段仅输入<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>T</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">T_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>时刻信息，第二阶段仅输入<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>T</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">T_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.13889em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>时刻信息，当T2输入时，若内部状态有变化（即对应T1,T2之间的像素变化），利用peephole connections可以很快的将其传递至各个门。</p>
<p><img src="https://z3.ax1x.com/2021/04/21/cHj7K1.jpg" alt="" /></p>
<p>上图显示了一个隐藏层中的结构。分T1和T2两步。</p>
<h4 id="lstm2"><a class="markdownIt-Anchor" href="#lstm2"></a> LSTM2</h4>
<blockquote>
<p>Mou, Lichao, Lorenzo Bruzzone, and  Xiao Xiang Zhu. “Learning spectral-spatial-temporal features via a  recurrent convolutional neural network for change detection in  multispectral imagery.” <em>IEEE Transactions on Geoscience and Remote Sensing</em> 57.2 (2018): 924-935.</p>
<p>cited times: 151</p>
</blockquote>
<p>改文章提出了递归卷积神经网络(ReCNN)结构。分为CNN, RNN, FCN三个部分。CNN采用扩张卷积的形式。</p>
<p>RNN的隐藏层：</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi mathvariant="bold">h</mi><mi>t</mi></msub><mo>=</mo><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mn>0</mn><mspace width="1em"/><mi>i</mi><mi>f</mi><mspace width="1em"/><mi>t</mi><mo>=</mo><mn>0</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>φ</mi><mo stretchy="false">(</mo><msub><mi mathvariant="bold">h</mi><mrow><mi>t</mi><mo>−</mo><mn>1</mn></mrow></msub><mo separator="true">,</mo><msup><mi>f</mi><msub><mi>T</mi><mi>t</mi></msub></msup><mo stretchy="false">)</mo><mspace width="1em"/><mi>e</mi><mi>l</mi><mi>s</mi><mi>e</mi></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">\mathbf{h}_t==\left\{\begin{matrix}
0 \quad if \quad t=0\\ 
\varphi (\mathbf{h}_{t-1},f^{T_t}) \quad else
\end{matrix}\right.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord"><span class="mord mathbf">h</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span></span><span class="base"><span class="strut" style="height:0.36687em;vertical-align:0em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.401331em;vertical-align:-0.9506654999999999em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">{</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.4506655em;"><span style="top:-3.6106654999999996em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0</span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathdefault">i</span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord">0</span></span></span><span style="top:-2.4093345em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">φ</span><span class="mopen">(</span><span class="mord"><span class="mord"><span class="mord mathbf">h</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">t</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.29634285714285713em;"><span style="top:-2.357em;margin-left:-0.13889em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathdefault">e</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">s</span><span class="mord mathdefault">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9506654999999999em;"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<p>同时提出了用LSTM作RNN结构的途径，大同小异不再赘述。</p>
<h3 id="gan"><a class="markdownIt-Anchor" href="#gan"></a> GAN</h3>
<blockquote>
<p>Gong, Maoguo, et al. “Generative adversarial networks for change detection in multispectral imagery.” <em>IEEE Geoscience and Remote Sensing Letters</em> 14.12 (2017): 2310-2314.</p>
<p>cited times: 51</p>
</blockquote>
<p>大同小异，略。</p>
<h2 id="常用数据与数据集"><a class="markdownIt-Anchor" href="#常用数据与数据集"></a> 常用数据与数据集</h2>
<p>在change detection这一领域，常用数据类型为光学RS图像、SAR图像和街景图像。下图展示了change detection常用数据类型(a,b,f)及其他补充数据类型</p>
<img src="https://z3.ax1x.com/2021/04/21/cHjbb6.jpg" alt="7" style="zoom: 33%;" />
<p>高光谱是由数百个光谱波段组成的体积图像立方体。它们在电磁波谱的很大一部分上有窄带；波段范围一般小于10 nm。多光谱图像通常包含多个波段，但少于15个波段。多光谱图像的光谱分辨率为波长的0.1倍。全色图像只有一个波段，它是利用可见光谱中的总光能形成的(而不是把它划分成不同的光谱)。<strong>针对不同类型的图像需要不同的检测方法</strong>。</p>
<ul>
<li>在深度学习应用于高光谱变化检测这一领域，面临的问题有：数据维度过高，混合像素，高计算成本，和有限的训练数据集等。</li>
<li>多光谱图像的获取成本低且稳定，空间分辨率从低到高不等。它们可以提供丰富的颜色、纹理和其他属性。高空间分辨率或非常高空间分辨率(10 ~ 100  cm/pixel)的图像也能反映地物的结构信息。因此，<strong>多光谱图像被广泛地用于变化检测。</strong></li>
<li>全色图像只有一个波段(即黑白波段)，通常包含几百纳米的带宽。带宽使它能够保持一个高信噪比，使全色数据在一个高和非常高的空间分辨率可用。因此，通常将全色图像与多光谱图像进行融合，以获得更丰富的光谱信息和空间信息，用于高空间分辨率和极高空间分辨率的变化检测。也可以直接用于变化检测。</li>
</ul>
<p>光学遥感图像提供了丰富的光谱和空间信息，被广泛应用于变化检测。然而，光学传感器依赖于太阳的照明，使用的波长接近可见光或1毫米。因此，它们经常受到太阳辐射和云层的影响。另一方面，SAR使用的波长为1厘米到1米，并有自己的照明源。因此，它可以在几乎所有的天气条件下白天和晚上成像。</p>
<p>SAR图像往往受到散斑噪声的影响，使得变化检测过程比光学遥感图像更加困难。他们的三个关键问题包括</p>
<ol>
<li>抑制散斑噪声;</li>
<li>设计变更指标或者变更指标;</li>
<li>使用基于变更度量的阈值或分类器来生成最终的变更映射。</li>
</ol>
<p>使用人工智能技术，特别是自编码器和卷积神经网络来抑制斑点噪声和提取特征的变化检测方法已被证明是最先进的技术。</p>
<p>常用数据集：</p>
<img src="https://z3.ax1x.com/2021/04/21/cHjOUO.md.jpg" style="zoom:25%;" />
<img src="https://z3.ax1x.com/2021/04/21/cHjX5D.jpg" style="zoom:25%;" />
<h2 id="现阶段框架"><a class="markdownIt-Anchor" href="#现阶段框架"></a> 现阶段框架</h2>
<p><img src="https://z3.ax1x.com/2021/04/21/cHjvPe.jpg" alt="" /></p>
<p>上图为变化检测的原理图，基于传统方法与基于AI方法。</p>
<p>看到Traditional change detection中的肉色框，列举了常用的传统检测方法：</p>
<ul>
<li>visual analysis: 由专家进行分析；</li>
<li>algebra-based: 基于代数方法，图像差分，图像回归，图像比例，变化向量分析等；</li>
<li>Transformation: 变换方法，有PCA主成分分析，KT变化，多元变化检测MAD等；</li>
<li>classification: 基于分类的方法；</li>
<li>advanced: 采用先进的模型，如Li-Strahler反射率模型、光谱混合模型、生物物理参数法等，将多周期数据的光谱反射率值转换为基于物理的参数或分数，进行变化分析，更加直观，具有物理意义。但这是复杂和耗时的</li>
<li>其他:使用混合方法和其他方法，如基于知识、基于空间统计以及综合GIS和RS方法</li>
</ul>
<h3 id="ai-based-检测流程"><a class="markdownIt-Anchor" href="#ai-based-检测流程"></a> AI-based 检测流程</h3>
<p><img src="https://z3.ax1x.com/2021/04/21/cHjz2d.md.jpg" alt="" /></p>
<h3 id="框架"><a class="markdownIt-Anchor" href="#框架"></a> 框架</h3>
<h3 id="single-stream-framework"><a class="markdownIt-Anchor" href="#single-stream-framework"></a> Single-Stream Framework</h3>
<ul>
<li>
<p>Direct Classification Structure</p>
<p>将多个时相的图像进行融合，然后送入分类器进行学习，生成change map。重点在于fusion和classifier的选择。常见的fusion的方法有变化分析方法和直接连接方法。变化分析方法例如：CVA, differencing by log-ratio operator和change measures</p>
<p>直接拼接法可以保留多周期数据的全部信息，因此变化信息由后续分类器提取。一般情况下，一维输入数据直接串接，二维数据通过通道串接。此外也有原始数据与查分数据的融合。</p>
</li>
<li>
<p>Mapping Transformation-Based Structure</p>
<p>主要思想是利用AI方法学习特征映射变换，并利用它对一类数据进行特征变换。转换后的特征对应于另一种数据的特征。简而言之，它将数据从一个特征空间转换到另一个特征空间。最后，通过对两种数据的对应特征进行决策分析，可以得到变化图。</p>
</li>
</ul>
<img src="https://z3.ax1x.com/2021/04/21/cHv9KI.jpg" style="zoom:33%;" />
<h3 id="double-stream-framework"><a class="markdownIt-Anchor" href="#double-stream-framework"></a> Double-Stream Framework</h3>
<img src="https://z3.ax1x.com/2021/04/21/cHvCrt.jpg" style="zoom:33%;" />
<p>双通道的检测框架如上图所示，这符合change detection任务的多时相特性。两个网络分别提取其特征。(a)展示了孪生网络与决策模型的检测框架；(b)展示了迁移学习形式的框架。采用预先训练好的AI模型作为特征提取器，用于生成两个时期的特征图，两个时期的特征提取器可以相同；©展示了后分类模型的框架，基本是对两张图像分别进行分类任务然后比较，可以看做是post classification方法的一种。</p>
<h2 id="change-map的生成方案"><a class="markdownIt-Anchor" href="#change-map的生成方案"></a> Change map的生成方案</h2>
<p>基于阈值的方法：以最简单的像素灰度差值为例，设定某一阈值，高于该阈值的被标记为已变化，低于标记为未变化。因此，一般而言是针对像素某一特征的数值来进行二分类任务。</p>
<p>基于聚类的方法：例如前文中提到的DBN在change detection任务中的应用，DBN作为一种特征提取器得到对于每一个patch的向量描述，包含模值与方向，根据这两个信息采用聚类的方法以无监督的形式将图中像素自然聚成多类。</p>
<p>基于分类器的方法：举例为基于深度模型训练一个分类器，标签即已变化或者未变化，训练后根据分类器的输出来生成change map</p>
<p>基于分类后比较的方法：该方法是对原始图像进行语义分割，根据每一部分的语义信息是否变化来得到change map</p>
<h2 id="参考文献"><a class="markdownIt-Anchor" href="#参考文献"></a> 参考文献</h2>
<ol>
<li>
<p>一个关于遥感领域change detection的survey（2018）</p>
<blockquote>
<p>Asokan, Anju, and J. Anitha. “Change detection techniques for remote sensing applications: a survey.” <em>Earth Science Informatics</em> 12.2 (2019): 143-160.</p>
<p>cited times: 44</p>
</blockquote>
</li>
<li>
<p>针对多时相高光谱图像变化检测的综述</p>
<blockquote>
<p>Liu, Sicong, et al. “A review of change detection in multitemporal  hyperspectral images: Current techniques, applications, and challenges.” <em>IEEE Geoscience and Remote Sensing Magazine</em> 7.2 (2019): 140-158.</p>
<p>cited times: 47</p>
</blockquote>
</li>
<li>
<p>基于人工智能技术的前沿change detection检测技术综述</p>
<blockquote>
<p>Shi, Wenzhong, et al. “Change detection based on artificial intelligence: State-of-the-art and challenges.” <em>Remote Sensing</em> 12.10 (2020): 1688.</p>
<p>cited times: 20</p>
</blockquote>
</li>
<li>
<p>（国内参考文献）多时相变化检测</p>
<blockquote>
<p>张良培 &amp; 武辰.(2017).多时相遥感影像变化检测的现状与展望. <em>测绘学报</em>(10),1447-1459. doi:CNKI:SUN:CHXB.0.2017-10-028.</p>
</blockquote>
</li>
<li>
<p>（国内参考文献）多时相变化检测方法综述</p>
<blockquote>
<p>眭海刚,冯文卿,李文卓,孙开敏 &amp; 徐川.(2018).多时相遥感影像变化检测方法综述. <em>武汉大学学报(信息科学版)</em>(12),1885-1898. doi:10.13203/j.whugis20180251.</p>
</blockquote>
</li>
<li>
<p>Gabor小波与聚类</p>
<blockquote>
<p>Li, Heng-Chao, et al. “Gabor feature based unsupervised change detection of multitemporal SAR images based on two-level clustering.” <em>IEEE Geoscience and Remote Sensing Letters</em> 12.12 (2015): 2458-2462.</p>
</blockquote>
</li>
</ol>

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            <p>原文作者：<a href="http://xiuzhedorothy.gitee.io">宇航猫休蛰</a>
            <p>原文链接：<a href="http://xiuzhedorothy.gitee.io/2021/04/21/ying-xiang-bian-hua-jian-ce-zong-shu/">http://xiuzhedorothy.gitee.io/2021/04/21/ying-xiang-bian-hua-jian-ce-zong-shu/</a>
            <p>发表日期：<a href="http://xiuzhedorothy.gitee.io/2021/04/21/ying-xiang-bian-hua-jian-ce-zong-shu/">April 21st 2021, 10:03:40 am</a>
            <p>更新日期：<a href="http://xiuzhedorothy.gitee.io/2021/04/21/ying-xiang-bian-hua-jian-ce-zong-shu/">April 21st 2021, 10:32:17 am</a>
            <p>版权声明：本文采用<a rel="license noopener" href="http://creativecommons.org/licenses/by-nc/4.0/" target="_blank">知识共享署名-非商业性使用 4.0 国际许可协议</a>进行许可</p>
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        <ol class="toc"><li class="toc-item toc-level-1"><a class="toc-link" href="#影像变化检测研究综述"><span class="toc-number">1.</span> <span class="toc-text"> 影像变化检测研究综述</span></a><ol class="toc-child"><li class="toc-item toc-level-2"><a class="toc-link" href="#传统变化检测方法"><span class="toc-number">1.1.</span> <span class="toc-text"> 传统变化检测方法</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#直接比较法"><span class="toc-number">1.1.1.</span> <span class="toc-text"> 直接比较法</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#图像变换类方法"><span class="toc-number">1.1.2.</span> <span class="toc-text"> 图像变换类方法</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#分类后比较法"><span class="toc-number">1.1.3.</span> <span class="toc-text"> 分类后比较法</span></a></li></ol></li><li class="toc-item toc-level-2"><a class="toc-link" href="#对象级变化检测"><span class="toc-number">1.2.</span> <span class="toc-text"> 对象级变化检测</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#基于深度学习的变化检测"><span class="toc-number">1.3.</span> <span class="toc-text"> 基于深度学习的变化检测</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#autoencoder"><span class="toc-number">1.3.1.</span> <span class="toc-text"> Autoencoder</span></a><ol class="toc-child"><li class="toc-item toc-level-4"><a class="toc-link" href="#stacked-denoising-aes"><span class="toc-number">1.3.1.1.</span> <span class="toc-text"> stacked denoising AEs</span></a></li><li class="toc-item toc-level-4"><a class="toc-link" href="#daepropose-sccn"><span class="toc-number">1.3.1.2.</span> <span class="toc-text"> DAE(propose SCCN):</span></a></li></ol></li><li class="toc-item toc-level-3"><a class="toc-link" href="#deep-belief-network"><span class="toc-number">1.3.2.</span> <span class="toc-text"> Deep belief Network</span></a><ol class="toc-child"><li class="toc-item toc-level-4"><a class="toc-link" href="#rbm"><span class="toc-number">1.3.2.1.</span> <span class="toc-text"> RBM:</span></a></li><li class="toc-item toc-level-4"><a class="toc-link" href="#dbn"><span class="toc-number">1.3.2.2.</span> <span class="toc-text"> DBN:</span></a></li></ol></li><li class="toc-item toc-level-3"><a class="toc-link" href="#cnn"><span class="toc-number">1.3.3.</span> <span class="toc-text"> CNN</span></a><ol class="toc-child"><li class="toc-item toc-level-4"><a class="toc-link" href="#pca-net"><span class="toc-number">1.3.3.1.</span> <span class="toc-text"> PCA-Net</span></a></li><li class="toc-item toc-level-4"><a class="toc-link" href="#region-cnn"><span class="toc-number">1.3.3.2.</span> <span class="toc-text"> Region-CNN</span></a></li><li class="toc-item toc-level-4"><a class="toc-link" href="#unet"><span class="toc-number">1.3.3.3.</span> <span class="toc-text"> UNet++</span></a></li></ol></li><li class="toc-item toc-level-3"><a class="toc-link" href="#lstm"><span class="toc-number">1.3.4.</span> <span class="toc-text"> LSTM</span></a><ol class="toc-child"><li class="toc-item toc-level-4"><a class="toc-link" href="#improved-lstm"><span class="toc-number">1.3.4.1.</span> <span class="toc-text"> improved LSTM</span></a></li><li class="toc-item toc-level-4"><a class="toc-link" href="#lstm2"><span class="toc-number">1.3.4.2.</span> <span class="toc-text"> LSTM2</span></a></li></ol></li><li class="toc-item toc-level-3"><a class="toc-link" href="#gan"><span class="toc-number">1.3.5.</span> <span class="toc-text"> GAN</span></a></li></ol></li><li class="toc-item toc-level-2"><a class="toc-link" href="#常用数据与数据集"><span class="toc-number">1.4.</span> <span class="toc-text"> 常用数据与数据集</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#现阶段框架"><span class="toc-number">1.5.</span> <span class="toc-text"> 现阶段框架</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#ai-based-检测流程"><span class="toc-number">1.5.1.</span> <span class="toc-text"> AI-based 检测流程</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#框架"><span class="toc-number">1.5.2.</span> <span class="toc-text"> 框架</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#single-stream-framework"><span class="toc-number">1.5.3.</span> <span class="toc-text"> Single-Stream Framework</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#double-stream-framework"><span class="toc-number">1.5.4.</span> <span class="toc-text"> Double-Stream Framework</span></a></li></ol></li><li class="toc-item toc-level-2"><a class="toc-link" href="#change-map的生成方案"><span class="toc-number">1.6.</span> <span class="toc-text"> Change map的生成方案</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#参考文献"><span class="toc-number">1.7.</span> <span class="toc-text"> 参考文献</span></a></li></ol></li></ol>
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